|Description||In this work we examine a system consisting of a confined one-dimensional arrangement of atoms that
we describe by using the 2-dimensional CPN−1 model, restricted to an interval and at finite temperature.
We develop a method to obtain the bulk and boundary parts of the one-loop effective action as a function of the effective mass of the fluctuations. The formalism has the advantage of allowing for a systematic
analysis of a large class of boundary conditions and to model the (adiabatic) response of the ground state to changes in the boundary conditions. In the case of periodic boundary conditions, we find that
inhomogeneous phases are disfavored for intervals of large size. Away from periodic boundary conditions,
our numerical results show that the ground state has a generic crystal-like structure that can be modulate by variations of the boundary conditions. The results presented here could be relevant for experimental
implementations of nonlinear sigma models and could be tested by lattice numerical simulations.||en_US